Solving First-Order Constraints over the Monadic Class

First-order constraints over arbitrary theories or structures can be formalised as the formula instantiation problem as defined in [11]. Several re- sults have been previously obtained for the formula instantiation problem in the case of quantifier-free formulas of first-order logic. In this paper we prove the first general result on formula instantiation for quantified formulas, namely that formula instantiation is decidable for the monadic class without equality.

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